Perturbation Method for Analyzing the Effect on Ultrasonic Echo Returns on Rough Surfaces in Material Cracks and Voids

In this paper, elastic wave scattering from rough surfaces and rough cracks is investigated theoretically. Two approaches based on the reciprocity relation a re developed. In one of them, the s cattering coefficient is expressed in terms of the normal stress on a reference surface in the presence o f the roughness and is approximated by an equivalent boundary condition in terms of the first order perturbation in stress field (Brekhovskikh's boundary condition). In the other, t he formulation is performed in terms of the velocity d istribution on rough surface and various approximation t echniques are discussed. The results are compared and examples are given. X